Seeley suggests dancing is regulated by efficiency: \(\frac{gain-cost}{cost}\).

• Gain is determined by the nectar quality of the flower, \(q\).
• Cost is determined by the distance to the flower, \(x\).
• Energy gained is therefore \(\propto\) \(q\), cost increases linearly with \(x\).
• Can therefore refactor efficiency as: \(\frac{q}{1+\alpha x} - 1\), where \(\alpha\) is the energy spend per unit of distance.
• Energy spend cannot be negative, so the function must be positive:

\[\sigma(q,x) = [\frac{q}{1+\alpha x}-1]_+\]

• Assume scouts search an environment without information and report back the first resource found.
• Floral resources should be randomly distributed around a hive and thus follow a Poisson distribution.
• The distance between a central hive and each point should therefore be exponentially distributed, with rate \(\lambda_s\).
• This scout distribution is altered by the profitability function, which translates the distance of the resource to a number of dances reported on the dance floor.
• \(\sigma(q, x) \lambda_s e^{-\lambda_s x}\)

• Recruits sample randomly from the dance on the dance floor (scouts + other recruits).
• Recruits over-represent the best resources, skewing the distribution of dances.
• The best resource is implicitly a function of distance and should bias towards the closest patches to the colony.
• The chance of discovering a food source within a radius of \(x\) in a circular area is: \(e^{-\lambda_r \pi x^2}\), where \(\lambda_r\) is the scout discovery rate.

• The distribution of the nearest food sources that recruits would come for is: \(2 \lambda_r \pi x e^{-\lambda_r \pi x^2}\)

• \(\sigma(q, x) 2 \lambda_r \pi x e^{-\lambda_r \pi x^2}\)

• The distribution of reported distances is a superposition of recruit and scout distance distributions.
• \(p\) provides a proportional weighting of the number of dances coming from either a scout or recruit strategy.

Are different foraging strategies identifiable from the distribution of foraging distances reported on the dance floor?

We created an Agent Based Simulation of a foraging honey bee colony.

1. Hive exists surrounded by resources which have a quality and distance from the hive. The resources are randomly removed and others added for simulate flower turnover.
2. A proportion of foragers act as scouts, leave the hive on a randomly determined path and report back the first patch discovered.
3. The rest act as recruits and sample randomly the pooled dances of scouts and other recruits. Once they have a location they visit that resource and also advertise it.
4. Scouts and recruits return to their flower but once that patch disappears they must return to searching or following dances respectively.

A. Outline of scout foraging. Scouts leave the hive on a random flight path (white lines) and continue until they encounter a resource (flowers in the figure). B. Outline of foraging with recruitment. Scouts continue to identify resources but recruits’ sample available dances provided by recruits and other scouts. C. Log inverse frequency distribution of foraging distances reported by scouts. D. Log inverse frequency distribution of foraging distances reported by recruits.

• Different foraging strategies leave different patterns in the distribution of foraging distances reported on the dance floor.

• Logic of the model holds water.

Do colonies in real world environments forage collectively, individually or through some other mechanism?

• Waggle dance data was collected and decoded from 10 urban and 10 agri-rural sites over the 2017 season for a total of > 3000 dances (Credit: Ash Samuelson).
• Fit our full model to the distribution of foraging distances recorded for each site.
• Also fit a scouts only model (\(p\) fixed to 1) to evaluate an individual only foraging strategy.
• Model selection used to determine which strategy was more likely.
• Model fit used to determine if our model offered a good explanation of the data.

• We have successfully translated the dominant theoretical understanding of honeybee foraging into a quantifiable and thus measurable model.
• Evaluated this model against a large empirical dataset to show that in the majority of cases it provides an extremely good explanation of foraging patterns.
• In some cases, a model of individual behaviour is more suitable
• Provides new evidence that honeybees can regulate the use of the waggle dance and use personal rather than social information at a colony level.
• Provides a new, non-invasive tool to evaluate what factors might influence how honeybees use the waggle dance.

• Environmental factors are thought to influence the use of the waggle dance and social information more broadly.
• Intensely studied in honeybees using theoretical and empirical studies.
• Empirical methods are open to problems.
• Our model provides a new way of doing things.
• Fitting our model to data gives us a proportion of scout dances \(p\), providing an estimate of what the foragers are doing (working alone or following others) based on what they report.

• No real difference in the proportion of scouts between Agri-rural and Urban areas.

• The foraging land around each site was classified by their different land-use types (Credit: Ash Samuelson)

• Urban: continuous central, dense residential, sparse residential, parks allotments cemeteries, amenity.grassland, Railway, woodland, and water.

• Agri-rural: woodland, Non agricultural unmanaged green space, Non, agricultural managed green space, arable, pasture, other agricultural, fruit, Oil Seed Rape, built up area, and water.

Is there a relationship between land-use type and proportion of scouts?

• PC1, explaining ~61% of the variance in the proportion of scouts, correlates:
• Positively with continuos central land, dense residential and water.
• Negatively with sparse residential and amenity grassland.

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• Land-use type has a significant impact of the proportion of scouts.
• Reinforces the idea that the waggle dance is used flexibly in certain environments.
• Suggests agricultural land pressures colonies to use more scout type strategies.

more implications…finish up.